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Results tagged with lo.logic
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user 165275
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.
11
votes
What can be preserved in mathematics if all constructions are carried out in ZF?
One of the standard texts which presents functional analysis only based on ZF+DC is the monograph (consisting of 3 volumes) Henry G. Garnir, Marc de Wilde, and Jean Schmets, Analyse Fonctionnelle.
Als …
- 1,869
4
votes
Simpler proofs using the axiom of choice
For an orthomorphism $A$ in a (real or complex) Banach lattice $X$ the formula $\lvert A\rvert x=\lvert Ax\rvert$ for $x\ge0$ can be obtained relatively quickly if one uses the fact that $X$ is order …
2
votes
Standard models of N and R: An Alice/Bob approach
This is way too long for a remark, therefore I post it as an answer.
Although I agree with the previous answers that there is probably no clear “intended” model of set theory, there are perhaps two pr …
- 1,869
1
vote
The Tarski-Lindenbaum theorem of the middle value
Not a very satisfactory answer, but some considerations to the proof of the MV theorem:
One might think that analogously to the proof of CBS (see e.g. Joel David Hamkins answer how to use KT for that …
- 1,869