¿Is there a minimal standard model for ZFC?

Click For Summary

Discussion Overview

The discussion revolves around the existence of a minimal standard model for Zermelo-Fraenkel set theory with the Axiom of Choice (ZFC). Participants explore whether such a model exists and what sets may or may not be included within it, focusing on definability and the characteristics of models in set theory.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant questions if there is a minimal standard mathematical model for Zermelo set theory that is contained within other models.
  • Another participant provides a reference link, possibly to a relevant academic paper or resource.
  • Several participants inquire about examples of sets that are not included in the minimal model of ZFC, indicating a search for clarification on the model's limitations.
  • One participant expresses uncertainty about whether all definable sets are included in the minimal model of ZFC.
  • A later post reformulates the question to ask if there are sets that can be defined in the minimal model of ZC but are not actually present in that model.

Areas of Agreement / Disagreement

The discussion remains unresolved, with participants expressing differing views and questions about the nature of sets in relation to the minimal model of ZFC.

Contextual Notes

Participants have not reached consensus on the existence of a minimal model or the specific characteristics of sets within it. There are indications of missing assumptions and definitions that could clarify the discussion.

Garrulo
Messages
61
Reaction score
0
¿Is there a minimal standard methamatematical model for Zermelo set theory in the sense that the other models contains this model ?
 
Physics news on Phys.org
Are there examples of set that it isn´t in the minimal model of ZFC
 
Sorry for my bad english, but are there any example of a set which it isn´t in the minimal model of ZFC, or are there all the definable in this model?
 
Last edited:
I reformulate the question: are there any set that it is definable in the minimal model of ZC but it isn´t in that model ??
 
Last edited:

Similar threads

Undergrad Direct limit of multiverse models of ZFC
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Higher Set Theory – Cantorian Sets / Large Cardinals in the Infinite
  • · Replies 5 ·
Replies
5
Views
1K
Graduate An additional constraint to the ZFC axioms?
  • · Replies 40 ·
2
Replies
40
Views
5K
Graduate Must all models of ZFC (in a standard formulation) be at least countable?
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Nonlinear Least Squares or OLS for Nonlinear Models?
  • · Replies 7 ·
Replies
7
Views
3K
Graduate Is there a decidable set theory?
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Scaling and Standardization in Statistical Analysis
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Maybe it is not necessary to define set membership?
  • · Replies 13 ·
Replies
13
Views
2K
Graduate On soundness and completeness of ZFC set theory
  • · Replies 6 ·
Replies
6
Views
2K
Graduate L and inaccessibles as models of ZFC
  • · Replies 4 ·
Replies
4
Views
3K