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Results tagged with set-theory
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user 22002
forcing, large cardinals, descriptive set theory, infinite combinatorics, cardinal characteristics, forcing axioms, ultrapowers, measures, reflection, pcf theory, models of set theory, axioms of set theory, independence, axiom of choice, continuum hypothesis, determinacy, Borel equivalence relations, Boolean-valued models, embeddings, orders, relations, transfinite recursion, set theory as a foundation of mathematics, the philosophy of set theory.
18
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3
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What notion captures the 'class' of all classes?
In ZFC there is no set that is the set of all sets, for this we introduce the notion of class. But then what is the 'class' of all classes, is it actually a class? Do we apply the same idea again? But …
- 2,369
4
votes
2
answers
744
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What is the impact on Godels theorem of Paraconsistency?
Russells paradox forced a restriction of the natural abstraction principle (that every predicate determines a set) so that Set Theory could be consistent. The standard one being ZF.
However paraconsi …
- 47.1k
0
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Essential reads in the philosophy of mathematics and set theory
Borges 'The Library of Babel' is a beautiful meditation on all sorts of philosophical positions around the 'idea' of infinity, epistemology, the sociology of science, set theory paradoxes. Its literat …
- 2,083
11
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2
answers
2k
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Are grothendieck universes enough for the foundations of category theory?
Grothendieck universes are equivalent to ZFC+a strongly inaccessible cardinal. This is low on the large cardinal axiom list. Is it enough to place category theory on a firm foundational basis, and how …
- 2,241
1
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2
answers
661
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How do we avoid circularity when we build a structure for ZFC? [closed]
when investigating ZFC as a formal language a structure is a set, are we not engaging in circular logic here? Or is 'set' thought of in a more primitive sense?
- 176