I'm trying to show that $\mathbb{Z}[x]^+ \models \mathsf{PA}^-$. What are the initial segments of this model?
2026-03-29 05:34:12.1774762452
Unconventional models and Peano Arithmetic
246 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in LOGIC
- Theorems in MK would imply theorems in ZFC
- What is (mathematically) minimal computer architecture to run any software
- What formula proved in MK or Godel Incompleteness theorem
- Determine the truth value and validity of the propositions given
- Is this a commonly known paradox?
- Help with Propositional Logic Proof
- Symbol for assignment of a truth-value?
- Find the truth value of... empty set?
- Do I need the axiom of choice to prove this statement?
- Prove that any truth function $f$ can be represented by a formula $φ$ in cnf by negating a formula in dnf
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?
To show that a certain model satisfies $PA^{-}$, make a list of all the axioms of $PA^{-}$ (they are the 15 axioms listed on the Wikipedia article). Then check, one at a time, that $\mathbb{Z}[x]^+$ satisfies each of these axioms.