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Results tagged with lo.logic
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user 15570
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.
17
votes
2
answers
1k
views
Is it consistent with ZFC that the real line is approachable by sets with no accumulation po...
Let $P$ denote the following proposition:
There exists a set $S$ of subsets of $\mathbb{R}$ such that
$S$ is totally ordered by inclusion;
each member of $S$ has no accumulation points;
the union of …
- 708
11
votes
3
answers
933
views
Some "axiom of choice" and "dependent choice" issues
I am probably about to ask some fairly basic questions, and yet I have found it quite hard to find the answers to these.
If I understand correctly, mathematicians tend to be quite happy working with …
- 708
8
votes
3
answers
690
views
Is "the purely probabilistic version of Freiling's axiom of symmetry" disprovable in ZFC?
I'm trying to pinpoint the "intuitive argument" for Freiling's Axiom of Symmetry. It's meant to be a "probabilistic" argument, so thinking about what seems to me to be the probabilistic intuition, it …
- 708
6
votes
1
answer
714
views
Which part(s) of this proof of Goodstein's Theorem are not expressible in Peano arithmetic?
EDIT: Noah Schweber helpfully points out that $\mathsf{ACA}_0$ is a conservative extension of Peano arithmetic in which certain aspects of my proof not expressible in Peano arithmetic are expressible. …
- 708
1
vote
2
answers
327
views
Heuristic interpretations of the PA-unprovability of Goodstein's Theorem
I've relatively recently learned about Goodstein's Theorem and its unprovability in Peano arithmetic (the Kirby-Paris Theorem). I do not have any real knowledge of formal logic; but I think I've seen …
- 708