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first-order and higher-order logic, model theory, set theory, proof theory, computability theory, formal languages, definability, interplay of syntax and semantics, constructive logic, intuitionism, philosophical logic, modal logic, completeness, Gödel incompleteness, decidability, undecidability, theories of truth, truth revision, consistency.
2
votes
Applications of set theory in physics
I don't know how important these papers are considered to be, but they are by a physicist and published in a (mathematical) physics journal:
http://scitation.aip.org/content/aip/journal/jmp/17/5/10.1 …
0
votes
Density character of a metric space is an Ulam number
An Ulam number is some authors' term for what is called "a cardinal smaller than the first real-valued measurable cardinal" by set theorists in general, or "a measure-free cardinal" by D. H. Fremlin ( …
2
votes
Nice algebraic statements independent from ZF + V=L (constructibility)
We can use a theorem of Eklof and Mekler to get a statement about abelian groups that is independent of $ZFC + V=L$ under the additional assumption that it is consistent that weakly compact cardinals …
11
votes
Who needs Replacement anyway?
Here's an example of a published, nontrivial use of the the product of the sequence $\{ V, V^{*}, V^{**}, \ldots \}$ in a functional analysis paper, for the specific case of $V = \mathbb{R}^{\mathbb{N …