All Questions
Tagged with theories-of-arithmetic forcing
5 questions
7
votes
0
answers
284
views
Generic behavior of "polynomialish" models of $\mathsf{Q}$
(This question was originally asked and bountied at MSE - with different notation, some more explicit arguments, and topology in place of forcing.)
Suppose $\mathcal{R}=(R_i)_{i\in\mathbb{N}}$ is a ...
- 20.7k
7
votes
2
answers
708
views
On a theorem of Zhang Jinwen about models of arithmetic
In the paper ''A Nonstandard Model of Arithmetic Constructed by means of Forcing Method'', Zhang Jinwen states the following in his abstract:
The first nonstandard model of arithmetic was given by ...
- 32.2k
1
vote
1
answer
311
views
Forcing the consistency of $ZF$ from a fragment of $ZF$
Implicit in the technique of forcing is the following relative consistency result:
If $\mathfrak M$$\vDash$$T$, and therefore $T$ is consistent (where $\mathfrak M$ is the ground model) then if $\...
- 6,132
6
votes
1
answer
209
views
Is $PRA$ + $TI({\epsilon_0})$ mutually interpretable with some theory in the language of set theory?
As is well known, the following theory is equiconsistent with $PA$:
$ZFC$ with the axiom of infinity replaced by its negation.
Since this theory is equiconsistent with $PA$, it would seem ...
- 6,132
10
votes
1
answer
761
views
Forcing, cuts, and Dedekind-finite cardinalities
Tl;dr version: there are two natural classes of cuts in the nonstandard model of arithmetic consisting of the Dedekind-finite sets (if, in fact, they constitute such a model); both these classes are ...
- 20.7k