9 дек. 2018 г. · I heard of infinitary logic. And as I understood it allows for statements of infinite length and proofs of infinite length but with some conditions.

21 окт. 2018 г. · Basically, infinitary logic pushes us into set theory to a degree which finitary logic doesn't. (Although we shouldn't take the absoluteness of ...

9 дек. 2012 г. · One of the problems of infinitary logic is that it is possible for compactness to fail in a spectacular way: for example, one can concoct an ...

18 июл. 2015 г. · I have heard a rumor that there is a proof system for certain infinitary logics, given by Carol Karp (?) in her thesis, but I can't find a copy.

11 июл. 2014 г. · By your definition, L∞,ω is not an abstract logic, because there are a proper class of L∞,ω-sentences. Indeed, L∞,ω contains first-order, ...

13 нояб. 2013 г. · The common definition of ω-logic (a.k.a Lω1,ω logic) is the usual first order logic allowing infinite conjunctions and infinite proof. Chang and ...

2 янв. 2023 г. · The axiom of choice comes in, stating that it is possible to obtain such a set (although there is no way to explain it to the butler in finite time).

14 апр. 2020 г. · Infintitary logic generalises first-order logic to allow formulas of infinite length. The most common way in which formulas can become infinite ...

2 окт. 2015 г. · Second, note that L∞∞ is the "smallest" infinitary logic which has this property! For each κ, we can find two non-isomorphic structures A ...

3 июл. 2023 г. · GPK+∞ is a positive set theory with a "positive comprehension" axiom schema, and we could replace it with an "infinitary positive comprehension" ...