Set theory and logic
... so-called first-order theories, that is, those axiomatic theories for which the predicate calculus of first order provides a logical base. Sections 4-7 give a rigorous account for first-order theories of the material discussed at the intuitive level in Chapter 5. Much of this has been available here ...
... so-called first-order theories, that is, those axiomatic theories for which the predicate calculus of first order provides a logical base. Sections 4-7 give a rigorous account for first-order theories of the material discussed at the intuitive level in Chapter 5. Much of this has been available here ...
EXHAUSTIBLE SETS IN HIGHER-TYPE
... Clearly, finite sets of computable elements are exhaustible. What may be rather unclear is whether there are infinite examples. Intuitively, there can be none: how could one possibly check infinitely many cases in finite time? This intuition is correct when K is a set of natural numbers: it is a the ...
... Clearly, finite sets of computable elements are exhaustible. What may be rather unclear is whether there are infinite examples. Intuitively, there can be none: how could one possibly check infinitely many cases in finite time? This intuition is correct when K is a set of natural numbers: it is a the ...
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 ...
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 ...
Foundations of Mathematics I Set Theory (only a draft)
... part of our book once we know what these objects are). It would be interesting to know what the reader things about the equality 2 = {0, 1}. Does it hold or not? It all depends on the definition of 2. As we will see in the next part, the integer 2 will be defined as the set {0, 1}, so that the equal ...
... part of our book once we know what these objects are). It would be interesting to know what the reader things about the equality 2 = {0, 1}. Does it hold or not? It all depends on the definition of 2. As we will see in the next part, the integer 2 will be defined as the set {0, 1}, so that the equal ...
Paradoxes in Logic, Mathematics and Computer Science
... These names are justified by the following: Fact: 1 < 0 < 1 Proof: Since 0 0, ({0},{}) ({},{}) = 0 is not true. Thus, ({},{}) < ({0},{}), i.e. 0 < 1. Also, ({},{}) ({},{0}) is not true. Thus, ({},{0}) < ({},{}), i.e. 0 < 1. However, ({0},{0}) is NOT a surreal number, since it is not true ...
... These names are justified by the following: Fact: 1 < 0 < 1 Proof: Since 0 0, ({0},{}) ({},{}) = 0 is not true. Thus, ({},{}) < ({0},{}), i.e. 0 < 1. Also, ({},{}) ({},{0}) is not true. Thus, ({},{0}) < ({},{}), i.e. 0 < 1. However, ({0},{0}) is NOT a surreal number, since it is not true ...
