Tagged Questions
1
vote
0answers
60 views
Is a “model” only a proper model if everything in it's definition is also explicitly constructed?
Say you have some collection of axioms and you find a set $X$ fulfilling them. And the definition of the set $X$ involves another concept, e.g. the real number, but only in a way which refers to the ...
2
votes
2answers
115 views
Forcing Question about a sequence of functions from $\aleph_{0}$ into $2 = \{0, 1\}$
I'm trying to go through Timothy Chow's A Beginner's Guide to Forcing (arxiv pdf).
My particular question is about the first paragraph of Section $5$ (on p. $7$ of the above pdf).
First, my vague ...
2
votes
2answers
119 views
Am I allowed to realize one object twice within one set-theory?
Say I consider a set theory with the Axioms of Extensionality and the Axiom of Pairing.
As I understand it, stating the axiom allows me to make a definition like
$$(a,b):=\{\{a\},\{a,b\}\}$$
and ...
1
vote
1answer
106 views
Can the ongoing need for a meta language be stopped by a loop?
As an afterthought to this question on sets in set theory, and more specifically to the observation that a (first-order) logic requires a meta-language to explain itself (i.e. there is already an ...
7
votes
2answers
347 views
Relationship between Category theory and Axiomatic set theory
I've recently started learning Category theory- and I have a pondering- wondering if anyone can help.
Is it possible for two categories to satisfy two different set-axiom system. Namely- is it ...
3
votes
2answers
467 views
A first order sentence such that the finite Spectrum of that sentence is the prime numbers
The finite spectrum of a theory $T$ is the set of natural numbers such that there exists a model of that size. That is $Fs(T):= \{n \in \mathbb{N} | \exists \mathcal{M}\models T : |\mathcal{M}| =n\}$ ...
