For first order logic without equality, what are the exact axioms we give to define the relation of equality ?
I can't find the exact axioms even in Wikipedia... Any reference to any article or a list of the exact axioms would do ...
2026-03-29 18:36:05.1774809365
Axioms for equality
68 Views Asked by user1203803 https://math.techqa.club/user/user1203803/detail AtRelated Questions in FIRST-ORDER-LOGIC
- Proving the schema of separation from replacement
- Find the truth value of... empty set?
- Exchanging RAA with double negation: is this valid?
- Translate into first order logic: "$a, b, c$ are the lengths of the sides of a triangle"
- Primitive recursive functions of bounded sum
- Show formula which does not have quantifier elimination in theory of infinite equivalence relations.
- Logical Connectives and Quantifiers
- Is this proof correct? (Proof Theory)
- Is there only a finite number of non-equivalent formulas in the predicate logic?
- How to build a list of all the wfs (well-formed sentences)?
Related Questions in RELATIONS
- How are these definitions of continuous relations equivalent?
- Is a relation on which every element is related with itself alone transitive?
- Relation power composition
- Order relation proof
- Order relation proof ...
- How to identify if a given Hasse diagram is a lattice
- Is the relation < a strict total order?
- Is there a name for this property on a binary relation?
- Finding all reflexive binary relations of a set
- Showing that a relation is reflexive, symmetric and transitive
Related Questions in AXIOMS
- Should axioms be seen as "building blocks of definitions"?
- Non-standard axioms + ZF and rest of math
- Does $\mathbb{R}$ have any axioms?
- Finite axiomatizability of theories in infinitary logic?
- Continuity axioms and completness axioms for real numbers are the same things?
- Why don't we have many non euclidean geometries out there?
- Why do we need the axiom of choice?
- What axioms Gödel is using, if any?
- Determine if U a subspace of $P_3$?
- Why such stark contrast between the approach to the continuum hypothesis in set theory and the approach to the parallel postulate in geometry?
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?