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Autor:
Button, Tim
Hilary Putnam once suggested that "the actual existence of sets as 'intangible objects' suffers... from a generalization of a problem first pointed out by Paul Benacerraf... are sets a kind of function or are functions a sort of set?" Sadly, he did n
Externí odkaz:
http://arxiv.org/abs/2401.00201
Autor:
Button, Tim
Consider a variant of the usual story about the iterative conception of sets. As usual, at every stage, you find all the (bland) sets of objects which you found earlier. But you also find the result of tapping any earlier-found object with any magic
Externí odkaz:
http://arxiv.org/abs/2308.06789
Autor:
Button, Tim
This document comprises Level Theory, parts 1-3. PART 1. The following bare-bones story introduces the idea of a cumulative hierarchy of pure sets: 'Sets are arranged in stages. Every set is found at some stage. At any stage S: for any sets found bef
Externí odkaz:
http://arxiv.org/abs/2103.06715
Autor:
Gorbow, Paul K., Leigh, Graham E.
We develop an untyped framework for the multiverse of set theory. $\mathsf{ZF}$ is extended with semantically motivated axioms utilizing the new symbols $\mathsf{Uni}(\mathcal{U})$ and $\mathsf{Mod}(\mathcal{U, \sigma})$, expressing that $\mathcal{U}
Externí odkaz:
http://arxiv.org/abs/2005.11087
Autor:
Morton, Anthony B.
It is well-known that the Continuum Hypothesis (CH) is independent of the other axioms of Zermelo-Fraenkel set theory with choice (ZFC). This raises the question of whether an intuitive justification exists for CH as an additional axiom, or conversel
Externí odkaz:
http://arxiv.org/abs/1311.0545
Autor:
Paul K. Gorbow, Graham E. Leigh
We develop an untyped framework for the multiverse of set theory.$\mathsf {ZF}$is extended with semantically motivated axioms utilizing the new symbols$\mathsf {Uni}(\mathcal {U})$and$\mathsf {Mod}(\mathcal {U, \sigma })$, expressing that$\mathcal {U
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::285ad877b1fba2e5a6ce628416c219fc
http://arxiv.org/abs/2005.11087
http://arxiv.org/abs/2005.11087