All Questions
62 questions
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Constructible cardinality downslides and their consistency strengths?
Posting "Large cardinals and constructible universe" mentions that $\omega_1^L < \omega_1$ if we assume Ramsey cardinal.
My question can we have more downslides like for example $\omega_2^...
- 11.3k
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191
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At which large cardinal, the theory of the minimal transitive model of ZFC starts proving its absence?
Let's take the minimal transitive model of $\sf ZFC$ which, I came to know, is some minimal $L_\kappa$ for a countable $\kappa$, that models $\sf ZFC$, and since its minimal so no subset of it can be ...
- 11.3k
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Further research on $\mathrm L_{\infty}$
In the mathoverflow question , "Godel's Constructible Universe in Infinitary Logics (A Possible Solution to $HOD$ Problem), Prof Hamkins answered user46667's question 2
What is $\mathrm L_{\infty}$?...
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What is the strength of this strict constructible iterative hierarchy?
Begin with the empty set then construct the set of the empty set, then construct the set of all subsets of the latter set, then at each level of construction construct the next level as the set all ...
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How does the cardinality of a set and its powerset compare in the hereditarily rank-concordant constructible world?
Working in the constructible universe "$L$", if we define two kinds of ranks for any constructible set $x$, one being the ordinal index of the first $L_\alpha$ where $x$ appears as a subset ...
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Can the Constructible Universe be built in absence of Unions and Power?
Can $L$ be built in
$\sf ZF$ $\sf-Regularity-Union-Power+ Boolean \ Union$?
We know that $L$ can be built in $\sf KP$, but here we don't have Set Union.
If the answer is to the negative, then would ...
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Must models of the following theory satisfying opposing infinitary sentences, satisfy opposing finitary sentences?
This is a follow-up to posting titled "Is this theory finitary first order complete?"
Recall the theory presented at that posting. Replace the size axiom by the following:
$\textbf{...
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Is Jensen's covering lemma meaningful in a platonist's view?
The typical applications of fine structure theory are finding out the lower bounds of consistency strength of axiom systems. In such a proccess, we also constructs many combinatorial objects in core ...
- 1,490
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Can Jensen's covering lemma be proven easier in generic extensions of L?
Jensen's covering lemma, stating that if there is no $0^\#$ in V, then some covering property holds true, has a very complex proof.
In any generic extension L[G] of L, $0^\#$ don't exist, so the ...
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Can all sets in stratified L above some stage be proximate?
Define stratified $L$, denoted by $^S L$, as:
Let $S$ be the set of all stratified formulas in first order language of set theory.
Define:
${ }^S Def (X) = \{\{y \in X \mid (X, \in) \models \phi(y,z_1,...
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Is "ZF+ V=L" an upper limit theory for cardinal decidability (per its strength)?
{EDIT: this posting has been edited, the additional text is in italics}
If $\varphi, \psi$ are two parameter free formulas in the language of set theory $T$ such that there is a theorem of $T$ that ...
- 11.3k
-2
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What does the Concordant constructible universe model?
Define a ranking function $\cal R$ as:
$\mathcal{R}: V \to ON; \,\mathcal {R}(x)= \min \alpha \, \forall y \in x: \alpha > \mathcal {R}(y) $
Now the constructible rank $\mathcal R^c$ of a set $X$ ...
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