A Survey on the Model Theory of Difference Fields - Library
... and stating elementary results, we discuss independence and the various concepts of rank, the dichotomy theorems, and, as an application, the Manin–Mumford conjecture over a number field. We conclude with some other applications. ...
... and stating elementary results, we discuss independence and the various concepts of rank, the dichotomy theorems, and, as an application, the Manin–Mumford conjecture over a number field. We conclude with some other applications. ...
Topological aspects of real-valued logic
... formalized by Lukasiewicz in the 1920’s for three truth values [80] and later infinitely many truth values [81]. Pavelka added rational constant connectives to the real-valued version of Lukasiewicz logic and proved a completeness theorem for the resulting Lukasiewicz-Pavelka logic [92, 93, 94]. Lat ...
... formalized by Lukasiewicz in the 1920’s for three truth values [80] and later infinitely many truth values [81]. Pavelka added rational constant connectives to the real-valued version of Lukasiewicz logic and proved a completeness theorem for the resulting Lukasiewicz-Pavelka logic [92, 93, 94]. Lat ...
REVERSE MATHEMATICS, WELL-QUASI
... and algebraic geometry but with the connections between Noetherian spaces and the theory of well-quasi-orders. Goubault-Larrecq in [GL07], motivated by possible applications to verification problems as explained in [GL10], provided several results demonstrating that Noetherian spaces can be thought ...
... and algebraic geometry but with the connections between Noetherian spaces and the theory of well-quasi-orders. Goubault-Larrecq in [GL07], motivated by possible applications to verification problems as explained in [GL10], provided several results demonstrating that Noetherian spaces can be thought ...
Sets, Logic, Computation
... facts, and a store of methods and techniques, and this text covers both. Some students won’t need to know some of the results we discuss outside of this course, but they will need and use the methods we use to establish them. The Löwenheim-Skolem theorem, say, does not often make an appearance in co ...
... facts, and a store of methods and techniques, and this text covers both. Some students won’t need to know some of the results we discuss outside of this course, but they will need and use the methods we use to establish them. The Löwenheim-Skolem theorem, say, does not often make an appearance in co ...
Proof analysis beyond geometric theories: from rule systems to
... on the existential variables: in left rules, we have a variable condition stating that these variables should not appear anywhere else in the rule (cf. Section 3 below). It is then seen that all the structural properties of the basic sequent calculi are maintained by the addition of rules that arise ...
... on the existential variables: in left rules, we have a variable condition stating that these variables should not appear anywhere else in the rule (cf. Section 3 below). It is then seen that all the structural properties of the basic sequent calculi are maintained by the addition of rules that arise ...
Cichon`s diagram, regularity properties and ∆ sets of reals.
... Far less is known concerning sets higher up in the projective hierarchy, even at the Σ13 and ∆13 levels. Concerning such questions, there are two, somewhat divergent, methods of approach. According to one of them, adopted e.g. by Ikegami in [24], Judah and Spinas in [31] and a few others, one assume ...
... Far less is known concerning sets higher up in the projective hierarchy, even at the Σ13 and ∆13 levels. Concerning such questions, there are two, somewhat divergent, methods of approach. According to one of them, adopted e.g. by Ikegami in [24], Judah and Spinas in [31] and a few others, one assume ...
Sets, Logic, Computation
... facts, and a store of methods and techniques, and this text covers both. Some students won’t need to know some of the results we discuss outside of this course, but they will need and use the methods we use to establish them. The Löwenheim-Skolem theorem, say, does not often make an appearance in co ...
... facts, and a store of methods and techniques, and this text covers both. Some students won’t need to know some of the results we discuss outside of this course, but they will need and use the methods we use to establish them. The Löwenheim-Skolem theorem, say, does not often make an appearance in co ...
Relevant deduction
... flawless way. From the formalized concept or principle logical consequences are then derived and retranslated into the natural language which are expected to give additional philosophical insights - until one suddenly recognizes that a conclusion is derivable which is intuitively nonsensical in a de ...
... flawless way. From the formalized concept or principle logical consequences are then derived and retranslated into the natural language which are expected to give additional philosophical insights - until one suddenly recognizes that a conclusion is derivable which is intuitively nonsensical in a de ...
The substitutional theory of logical consequence
... intended model would be the set-theoretic universe V . Of course there are also other motives for talking about the ‘set-theoretic universe’. Most set-theorists will happily talk about the set-theoretic universe, a cumulative hierarchy, and so on. There are ways to make this precise in a class theor ...
... intended model would be the set-theoretic universe V . Of course there are also other motives for talking about the ‘set-theoretic universe’. Most set-theorists will happily talk about the set-theoretic universe, a cumulative hierarchy, and so on. There are ways to make this precise in a class theor ...
Back to Basics: Revisiting the Incompleteness
... of arithmetic to be ω-consistent. And since ω-consistency is a matter of not being able to prove a certain combination, ω-consistency entails plain consistency. ...
... of arithmetic to be ω-consistent. And since ω-consistency is a matter of not being able to prove a certain combination, ω-consistency entails plain consistency. ...
TOWARD A STABILITY THEORY OF TAME ABSTRACT
... and Grossberg and VanDieren used Shelah’s proof (their actual initial motivation for isolating tameness) to show that the upward part of the transfer holds in tame AECs with amalgamation. Recently, the superstability theory of tame AECs with a monster model has seen a lot of development [Bon14a, Vas ...
... and Grossberg and VanDieren used Shelah’s proof (their actual initial motivation for isolating tameness) to show that the upward part of the transfer holds in tame AECs with amalgamation. Recently, the superstability theory of tame AECs with a monster model has seen a lot of development [Bon14a, Vas ...
Set theory
Set theory is the branch of mathematical logic that studies sets, which informally are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics. The language of set theory can be used in the definitions of nearly all mathematical objects.The modern study of set theory was initiated by Georg Cantor and Richard Dedekind in the 1870s. After the discovery of paradoxes in naive set theory, numerous axiom systems were proposed in the early twentieth century, of which the Zermelo–Fraenkel axioms, with the axiom of choice, are the best-known.Set theory is commonly employed as a foundational system for mathematics, particularly in the form of Zermelo–Fraenkel set theory with the axiom of choice. Beyond its foundational role, set theory is a branch of mathematics in its own right, with an active research community. Contemporary research into set theory includes a diverse collection of topics, ranging from the structure of the real number line to the study of the consistency of large cardinals.