منابع مشابه
Topological Models of Epistemic Set Theory
The standard set-theoretic formalization of classical mathematics is inadequate in the sense that it neglects the constructive aspect of ordinary mathematical practice. (For an extended argument to this effect, see [5].) Even classical mathematicians with no constructivistic scruples discuss what they can construct or compute. In a number of papers, including especially [3], I have proposed tha...
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The Boolean prime ideal theorem is a very slightly weaker version of the axiom of choice. In 2011, Andreas Blass showed that models of set theory (with atoms) in which the Boolean prime ideal theorem holds but the full axiom of choice fails correspond with a certain type of topological group. The path taken to prove this surprising result draws not just from set theory but also from combinatori...
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1. First order logic and the axioms of set theory 2 1.1. Syntax 2 1.2. Semantics 2 1.3. Completeness, compactness and consistency 3 1.4. Foundations of mathematics and the incompleteness theorems 3 1.5. The axioms 4 2. Review of basic set theory 5 2.1. Classes 5 2.2. Well-founded relations and recursion 5 2.3. Ordinals, cardinals and arithmetic 6 3. The consistency of the Axiom of Foundation 8 ...
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Article history: Received 17 April 2015 Received in revised form 18 June 2015 Accepted 6 July 2015 Available online 22 July 2015
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A model is said to be Leibnizian if it has no pair of indiscernibles. Mycielski has shown that there is a first order axiom LM (the LeibnizMycielski axiom) such that for any completion T of Zermelo-Fraenkel set theory ZF , T has a Leibnizian model iff T proves LM. Here we prove: Theorem A. Every complete theory T extending ZF + LM has 2 א 0 nonisomorphic countable Leibnizian models. Theorem B. ...
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ژورنال
عنوان ژورنال: Annals of Pure and Applied Logic
سال: 1990
ISSN: 0168-0072
DOI: 10.1016/0168-0072(90)90032-w