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Results tagged with lo.logic
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user 35626
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.
1
vote
How to prove that a binary relation is a strongly rigid relation? i.e. Polρ only contains pr...
I do not see an easy way to prove it. The characterization you mention was published
in the 1970's by Anne Fearnley, and the proof was a nicely organized but mildly tedious
examination of cases based …
- 2,158
2
votes
Axiomatization of first order logic (finitely many variables)
I have spent decades away from much of this material, so the following is
not an answer so much as a sequence of suggestions spinning off the
idea that the poster is looking for a finite axiomatizatio …
- 2,158
3
votes
Accepted
When are the congruence lattices nicer?
A congruence lattice of a universal algebra is a complete (therefore bounded) lattice, and is also algebraic (every element is a join of compact elements). As such, the collection C of congruence lat …
- 2,158
8
votes
Meta$^{n{-}th}$ mathematics
This is has been considered in philosophy perhaps even more so than mathematical logic. I would consider Lindstroem's theorem (roughly, first order logic is the strongest system in some sense for whi …
- 2,158
6
votes
Can We Decide Whether Small Computer Programs Halt?
On the flip side, one can write a program that does the
Collatz sequence or walks through an enumeration of
natural number vectors to see if it has a solution to some
Diophantine equation whose solubi …
- 2,158