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New posts in foundations
How "Principia Mathematica" builds foundations
logic
foundations
What formula of ZFC defines the set of natural numbers?
logic
model-theory
foundations
natural-numbers
Is there a contradiction hiding in this alternative set theory with 3 axioms?
logic
foundations
alternative-set-theories
Uncountable closed set of reals biject with reals without replacement or choice
set-theory
alternative-proof
axiom-of-choice
foundations
descriptive-set-theory
What of the "Sets, Classes, and Categories" approach to the foundations?
set-theory
category-theory
foundations
What is meant by "function" in the axiom schema of replacement.
elementary-set-theory
logic
foundations
Constructing a sequence up to infinity
logic
set-theory
first-order-logic
foundations
Reference request: definition of class
reference-request
set-theory
foundations
Models of set theory
set-theory
foundations
Why might Dieudonne have been "begging the question" by appealing to second-order Peano Axioms?
elementary-set-theory
logic
philosophy
foundations
peano-axioms
Why is something not a field if it's a proper class?
abstract-algebra
foundations
What precisely is lost when considering proper classes rather than sets?
logic
set-theory
category-theory
foundations
Are there any foundations in which the universe itself gets dynamically extended?
reference-request
logic
soft-question
foundations
Give a serious explanation of the difference between an equation and a function.
algebra-precalculus
definition
foundations
Founding Arithmetic on geometry
reference-request
logic
set-theory
philosophy
foundations
We need something more than the axioms of ZFC to prove the Dedekind completeness?
real-analysis
set-theory
foundations
Why should the underlying set of a model be a set?
logic
set-theory
model-theory
foundations
How strong is the axiom of well-ordered choice?
set-theory
axiom-of-choice
foundations
well-orders
How is geometry defined using ZFC?
geometry
set-theory
foundations
Does $\mathsf{ZFC} + \neg\mathrm{Con}(\mathsf{ZFC})$ suffice as a foundations of mathematics?
soft-question
philosophy
foundations
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