I am very interested in first order axiomatizations of the complex numbers, but I have never actually seen one laid out. Algebraically closed fields of characteristic zero are a start, but they don't have any axioms handling the real and imaginary parts, or any kind of metric/partial order. A field extension of real closed fields would probably do the job. Most articles on real closed fields mention that this is possible, but I haven't seen any that actually lay it out axiomatically. Could anyone point me to resources on the topic?
2026-04-13 19:44:23.1776109463
complex numbers from real closed fields
76 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in COMPLEX-NUMBERS
- Value of an expression involving summation of a series of complex number
- Minimum value of a complex expression involving cube root of a unity
- orientation of circle in complex plane
- Locus corresponding to sum of two arguments in Argand diagram?
- Logarithmic function for complex numbers
- To find the Modulus of a complex number
- relation between arguments of two complex numbers
- Equality of two complex numbers with respect to argument
- Trouble computing $\int_0^\pi e^{ix} dx$
- Roots of a complex equation
Related 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)?
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?