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New posts in peano-axioms
Really confused about the relationship between set theory, functions, ZFC, Peano axioms, etc.
logic
set-theory
definition
foundations
peano-axioms
Does ZFC prove a sentence in the language of arithmetic that PA+Con(ZFC) cannot prove?
logic
set-theory
peano-axioms
What is the difference between "Peano arithmetic," "second-order arithmetic," and "second-order Peano arithmetic?"
logic
axioms
foundations
peano-axioms
reverse-math
Is there an effective theory which "solves" the halting problem?
logic
computer-science
computability
peano-axioms
meta-math
Is it a paradox if I prove something as unprovable?
logic
proof-theory
peano-axioms
How do we know PA is incomparable with PRA + $\epsilon_0$?
logic
proof-theory
peano-axioms
ordinal-analysis
Why might Dieudonne have been "begging the question" by appealing to second-order Peano Axioms?
elementary-set-theory
logic
philosophy
foundations
peano-axioms
Why does the definition of addition require proofs?
real-analysis
peano-axioms
Why wouldn't someone accept Gentzen's consistency proof?
logic
proof-theory
peano-axioms
Presburger arithmetic
logic
proof-theory
peano-axioms
presburger-arithmetic
Who first proved Peano Arithmetic is not finitely axiomatizable?
logic
math-history
peano-axioms
Peano Arithmetic before Gödel
logic
math-history
peano-axioms
Gödel's Second Incompleteness Theorem and Arithmetically Non-Definable Theories
logic
computability
incompleteness
peano-axioms
Satisfaction of Peano postulates in topos with natural numbers object
peano-axioms
topos-theory
Can we prove that odd and even numbers alternate without using induction?
number-theory
logic
math-history
foundations
peano-axioms
Why are addition and multiplication included in the signature of first-order Peano arithmetic?
logic
peano-axioms
Why don't we use Presburger's arithmetic instead of Peano's arithmetic?
number-theory
logic
natural-numbers
foundations
peano-axioms
Model of Robinson Arithmetic but not Peano Arithmetic
logic
induction
model-theory
first-order-logic
peano-axioms
Why is it impossible to define multiplication in Presburger arithmetic?
logic
peano-axioms
presburger-arithmetic
How to express “b is a power of 10” – Typographical Number Theory in Gödel Escher Bach
number-theory
elementary-number-theory
logic
puzzle
peano-axioms
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