Why are the Peano axioms axioms for natural numbers if they have non-standard models? Shouldn't axioms determine an object up to isomorphism?
2026-03-29 10:49:02.1774781342
Why are the Peano axioms axioms for natural numbers if they have non-standard models?
87 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in MODEL-THEORY
- What is the definition of 'constructible group'?
- Translate into first order logic: "$a, b, c$ are the lengths of the sides of a triangle"
- Existence of indiscernible set in model equivalent to another indiscernible set
- A ring embeds in a field iff every finitely generated sub-ring does it
- Graph with a vertex of infinite degree elementary equiv. with a graph with vertices of arbitrarily large finite degree
- What would be the function to make a formula false?
- Sufficient condition for isomorphism of $L$-structures when $L$ is relational
- Show that PA can prove the pigeon-hole principle
- Decidability and "truth value"
- Prove or disprove: $\exists x \forall y \,\,\varphi \models \forall y \exists x \,\ \varphi$
Related Questions in PEANO-AXIOMS
- Difference between provability and truth of Goodstein's theorem
- How Can the Peano Postulates Be Categorical If They Have NonStandard Models?
- Show that PA can prove the pigeon-hole principle
- Peano Axioms and loops
- Is it true that $0\in 1$?
- Is there a weak set theory that can prove that the natural numbers is a model of PA?
- Exercises and solutions for natural deduction proofs in Robinson and Peano arithmetic
- Proof of Strong Induction Using Well-Ordering Principle
- Some questions about the successor function
- Prove addition is commutative using axioms, definitions, and induction
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
The original formulation of Peano-Dedekind axioms corresponds to modern Second Order Logic version.
Richard Dedekind in The Nature and Meaning of Numbers (Was sind und was sollen die Zahlen? (1888)), proved that they characterize the natural numbers up to isomorphism.