Show that if in the theory of $T$ every quantifier-free type has a unique extension to a complete type, then $T$ has quantifier elimination.
2026-03-25 09:32:26.1774431146
Quantifier Elimination in the quantifier free type
323 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 QUANTIFIER-ELIMINATION
- How quantifier elimination works
- Proof concerning quantifier elimination and substructures
- Show that the theory of $ (\mathbb{Z}, s)$ has quantifier elimination.
- Complete theory with quantifier elimination has finite boolean algebra
- Quantificational formatting and going from using logic with words, to using it for math proofs
- How much arithmetic is required to formalize quantifier elimination in Presburger arithmetic?
- If $T$ admits quantifier elimination in $\mathcal{L}$, does it admit quantifier elimination in $\mathcal{L}(c)$?
- Why is quantifier elimination desirable for a given theory?
- Exercise 3.4.3 in David Marker's "Model Theory"
- Quantifier elimination exercise
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?
Hint for abstract proof approach: continuous bijections between compact Hausdorff spaces are homeomorphisms, and the Stone Representation Theorem is true.
Hint for concrete proof approach: you're going to need to use the compactness theorem somewhere. Probably twice. Start by considering, for a formula $\varphi(x)$, the set of quantifier free formulas that $\varphi(x)$ implies.