A79 INTEGERS 13 (2013) - RIMS, Kyoto University
... where (q) is Euler’s totient function. Remark. Results similar to those in Theorems 1.1, 1.2, and 1.3 can be obtained by making use of Brun’s sieve. However, the constants will be weaker. To prove our theorem, we will rely on a judicious application of Selberg’s sieve. In particular, using either Se ...
... where (q) is Euler’s totient function. Remark. Results similar to those in Theorems 1.1, 1.2, and 1.3 can be obtained by making use of Brun’s sieve. However, the constants will be weaker. To prove our theorem, we will rely on a judicious application of Selberg’s sieve. In particular, using either Se ...
G - Courses
... terms according to the equalities between them in some structure satisfying the FO-sentence at hand. Here, we used the resolution procedure only for formulas of propositional logic. The resolution procedure can be extended to FO-formulas using unification of terms. There are other proofs of Göde ...
... terms according to the equalities between them in some structure satisfying the FO-sentence at hand. Here, we used the resolution procedure only for formulas of propositional logic. The resolution procedure can be extended to FO-formulas using unification of terms. There are other proofs of Göde ...
17 A Definition of Subjective Probability with F. J. Anscombe
... may be helpful. Our ‘‘horse lottery’’ corresponds to his ‘‘act’’; our ‘‘outcome of the race’’ to his ‘‘state of the world’’; our ‘‘prize’’ to his ‘‘consequence.’’ Of Savage’s six postulates, which he numbers P1 through P6, we share with him explicitly P1 (ordering of the horse lotteries—it is among ...
... may be helpful. Our ‘‘horse lottery’’ corresponds to his ‘‘act’’; our ‘‘outcome of the race’’ to his ‘‘state of the world’’; our ‘‘prize’’ to his ‘‘consequence.’’ Of Savage’s six postulates, which he numbers P1 through P6, we share with him explicitly P1 (ordering of the horse lotteries—it is among ...
Byzantine Agreement (BA) protocol
... players agreeing despite what the adversary says. If the honest players do not form a majority, it is in adversarial interest to send 0’s. ...
... players agreeing despite what the adversary says. If the honest players do not form a majority, it is in adversarial interest to send 0’s. ...
Notes on Writing Proofs
... rules of inference is best illustrated by an example. All men are mortal Socrates is a man Socrates is mortal In this example, the axioms (called premises or hypotheses) are written above the line and the theorem (called the conclusion) is written below the line. The whole argument is called a deduc ...
... rules of inference is best illustrated by an example. All men are mortal Socrates is a man Socrates is mortal In this example, the axioms (called premises or hypotheses) are written above the line and the theorem (called the conclusion) is written below the line. The whole argument is called a deduc ...
A Definition of Subjective Probability FJ Anscombe
... tickets of any sort under consideration. I n respect of preferences, we shall regard B as equivalent to ( l B ) , for any B. ...
... tickets of any sort under consideration. I n respect of preferences, we shall regard B as equivalent to ( l B ) , for any B. ...
Ordered Groups: A Case Study In Reverse Mathematics 1 Introduction
... Weak König’s Lemma. Every infinite binary branching tree has a path. The second subsystem of Z2 is called W KL0 and contains the axioms of RCA0 plus Weak König’s Lemma. Because the effective version of Weak König’s Lemma fails, W KL0 is strictly stronger than RCA0 . The best intuition for W KL0 ...
... Weak König’s Lemma. Every infinite binary branching tree has a path. The second subsystem of Z2 is called W KL0 and contains the axioms of RCA0 plus Weak König’s Lemma. Because the effective version of Weak König’s Lemma fails, W KL0 is strictly stronger than RCA0 . The best intuition for W KL0 ...
pdf
... might be thought of as an abstract object existing only in our minds, the fact is that mathematics advances only in so far as proofs are communicated. And writing remains the principal means of such communication. So to be a mathematician, you need to learn how to prove things but also to write thos ...
... might be thought of as an abstract object existing only in our minds, the fact is that mathematics advances only in so far as proofs are communicated. And writing remains the principal means of such communication. So to be a mathematician, you need to learn how to prove things but also to write thos ...
Saturation of Sets of General Clauses
... choose a fixed but arbitrary clause D ∈ N with C ∈ GΣ (D) and define sel′ (C ) to be those occurrences of literals that are ground instances of the occurrences selected by sel in D. Then proceed as in the proof of Cor. 3.27 using the above lifting lemma. ...
... choose a fixed but arbitrary clause D ∈ N with C ∈ GΣ (D) and define sel′ (C ) to be those occurrences of literals that are ground instances of the occurrences selected by sel in D. Then proceed as in the proof of Cor. 3.27 using the above lifting lemma. ...
03_MeasuringARs_maggie
... association rule in the form of X=>Y, where X and Y are sets of items. It can be read that, whenever a transaction T contains X, it probably will contain Y. Metrics: The probability is defined as the percentage of transactions containing Y in addition to X with respect to the overall number of tra ...
... association rule in the form of X=>Y, where X and Y are sets of items. It can be read that, whenever a transaction T contains X, it probably will contain Y. Metrics: The probability is defined as the percentage of transactions containing Y in addition to X with respect to the overall number of tra ...
1 Revenue Equivalence Theorem
... which is greater than the revenue of 1/3 for a standard auction. In general, we would like to answer the following question: is there an ”optimal” auction, in the sense that it maximizes revenue among all truthful mechanisms? Myerson showed that the answer is positive in the Bayesian setting even wh ...
... which is greater than the revenue of 1/3 for a standard auction. In general, we would like to answer the following question: is there an ”optimal” auction, in the sense that it maximizes revenue among all truthful mechanisms? Myerson showed that the answer is positive in the Bayesian setting even wh ...
On The Expressive Power of Three-Valued and Four
... by t and f , and two new ones: ?, that intuitively denotes lack of information (no knowledge), and >, that indicates inconsistency (\over"-knowledge). The truth values of Belnap's logic have two natural orderings: One, t , intuitively re ects di erences in the \measure of truth" that every value re ...
... by t and f , and two new ones: ?, that intuitively denotes lack of information (no knowledge), and >, that indicates inconsistency (\over"-knowledge). The truth values of Belnap's logic have two natural orderings: One, t , intuitively re ects di erences in the \measure of truth" that every value re ...
The average cost optimality equation
... as for zero-sum Markov games ([10], [15], [19]). A key property used in all of these papers, is that the imposed stability conditions yield the so-called weighted geometric ergodicity for the Markov chains induced by stationary policies. (The weighted geometric ergodicity is a generalization of the ...
... as for zero-sum Markov games ([10], [15], [19]). A key property used in all of these papers, is that the imposed stability conditions yield the so-called weighted geometric ergodicity for the Markov chains induced by stationary policies. (The weighted geometric ergodicity is a generalization of the ...
Probability Captures the Logic of Scientific
... . . . .3 A predicate followed by an individual constant means that the individual denoted by the individual constant has the property denoted by the predicate. For example, ‘F a3 ’ means that a3 has the property F. Let us define four predicates ‘Q1 ’ to ‘Q4 ’ in terms of ‘F ’ and ‘G’ by the followin ...
... . . . .3 A predicate followed by an individual constant means that the individual denoted by the individual constant has the property denoted by the predicate. For example, ‘F a3 ’ means that a3 has the property F. Let us define four predicates ‘Q1 ’ to ‘Q4 ’ in terms of ‘F ’ and ‘G’ by the followin ...
x 1 + x 2
... with a > 0 and b > 0 is called a CobbDouglas utility function (very useful family of functions, as it exhibits nice properties and serves several purposes). E.g. U(x1,x2) = x11/2 x21/2 (a = b = 1/2) V(x1,x2) = x1 x23 ...
... with a > 0 and b > 0 is called a CobbDouglas utility function (very useful family of functions, as it exhibits nice properties and serves several purposes). E.g. U(x1,x2) = x11/2 x21/2 (a = b = 1/2) V(x1,x2) = x1 x23 ...
On Equivalent Transformations of Infinitary Formulas under the
... (a) if a formula F is provable in the basic system then H ∪ {F } has the same stable models as H; (b) if F is equivalent to G in the basic system then H ∪ {F } and H ∪ {G} have the same stable models. Lemma 1. For any formula F and interpretation I, if I does not satisfy F then F I ⇒ ⊥ is a theorem ...
... (a) if a formula F is provable in the basic system then H ∪ {F } has the same stable models as H; (b) if F is equivalent to G in the basic system then H ∪ {F } and H ∪ {G} have the same stable models. Lemma 1. For any formula F and interpretation I, if I does not satisfy F then F I ⇒ ⊥ is a theorem ...
On Kronecker`s density theorem, primitive points and orbits of
... density theorem, see for instance [2], while the equivalence of (i) and (iv) is due to Dani and Raghavan, see Theorem 3.4 in [5]. The implications (iv) )(iii) ) (ii) are clear; observe that upon identifying an n ⇥ (m + n) matrix with the (m + n)-tuple of its columns, we have the inclusions XSLm+n (Z ...
... density theorem, see for instance [2], while the equivalence of (i) and (iv) is due to Dani and Raghavan, see Theorem 3.4 in [5]. The implications (iv) )(iii) ) (ii) are clear; observe that upon identifying an n ⇥ (m + n) matrix with the (m + n)-tuple of its columns, we have the inclusions XSLm+n (Z ...
The shape of incomplete preferences
... Y means that X is preferred or indifferent to Y, which is the behavioral primitive. The domain of % is the set of all lotteries. The asymmetric part of % is denoted by ≻, but it will not be used except in stating axiom A5. An extension of % is any preference relation %0 that is stronger in the sense ...
... Y means that X is preferred or indifferent to Y, which is the behavioral primitive. The domain of % is the set of all lotteries. The asymmetric part of % is denoted by ≻, but it will not be used except in stating axiom A5. An extension of % is any preference relation %0 that is stronger in the sense ...
on partially conservative sentences and interpretability
... 0. Introduction. Let T be a set of sentences. A sentence\- \p implies rhif
for every ifef
This
concept was introduced by Guaspari [2] and the basic existence theorems were
established by him and Solovay (cf. [2]). The first example of a ...
... 0. Introduction. Let T be a set of sentences. A sentence
Second-Order Logic and Fagin`s Theorem
... CHAPTER 7. SECOND-ORDER LOGIC AND FAGIN’S THEOREM The converse of Lynch’s Theorem is an open question: ...
... CHAPTER 7. SECOND-ORDER LOGIC AND FAGIN’S THEOREM The converse of Lynch’s Theorem is an open question: ...
in every real in a class of reals is - Math Berkeley
... so that the elements of M may be identi…ed with true subsets of N = N). As being an N model, or even also satisfying some 11 theory T , is clearly 11 in N , we immediately ...
... so that the elements of M may be identi…ed with true subsets of N = N). As being an N model, or even also satisfying some 11 theory T , is clearly 11 in N , we immediately ...
Kein Folientitel
... • Do only humans count? If yes: • Do only existing humans count? If yes: • Do only persons count? If yes: • Do persons always know best what is good for them? ...
... • Do only humans count? If yes: • Do only existing humans count? If yes: • Do only persons count? If yes: • Do persons always know best what is good for them? ...
