If we forbid existence of amorphous sets, then does that prove axiom of choice? Or some form of choice?
Where by a "form of choice" I mean something along those lines.
2026-04-09 08:01:44.1775721704
Does "ZF + no amorphous sets" implies some form of choice?
135 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in SET-THEORY
- Theorems in MK would imply theorems in ZFC
- What formula proved in MK or Godel Incompleteness theorem
- Proving the schema of separation from replacement
- Understanding the Axiom of Replacement
- Ordinals and cardinals in ETCS set axiomatic
- Minimal model over forcing iteration
- How can I prove that the collection of all (class-)function from a proper class A to a class B is empty?
- max of limit cardinals smaller than a successor cardinal bigger than $\aleph_\omega$
- Canonical choice of many elements not contained in a set
- Non-standard axioms + ZF and rest of math
Related Questions in CARDINALS
- Ordinals and cardinals in ETCS set axiomatic
- max of limit cardinals smaller than a successor cardinal bigger than $\aleph_\omega$
- If $\kappa$ is a regular cardinal then $\kappa^{<\kappa} = \max\{\kappa, 2^{<\kappa}\}$
- Intuition regarding: $\kappa^{+}=|\{\kappa\leq\alpha\lt \kappa^{+}\}|$
- On finding enough rationals (countable) to fill the uncountable number of intervals between the irrationals.
- Is the set of cardinalities totally ordered?
- Show that $n+\aleph_0=\aleph_0$
- $COF(\lambda)$ is stationary in $k$, where $\lambda < k$ is regular.
- What is the cardinality of a set of all points on a line?
- Better way to define this bijection [0,1) to (0,1)
Related Questions in AXIOM-OF-CHOICE
- Do I need the axiom of choice to prove this statement?
- Canonical choice of many elements not contained in a set
- Strength of $\sf ZF$+The weak topology on every Banach space is Hausdorff
- Example of sets that are not measurable?
- A,B Sets injective map A into B or bijection subset A onto B
- Equivalence of axiom of choice
- Proving the axiom of choice in propositions as types
- Does Diaconescu's theorem imply cubical type theory is non-constructive?
- Axiom of choice condition.
- How does Axiom of Choice imply Axiom of Dependent Choice?
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?
No, not at all.
The Cohen model, for example, does not have any amorphous sets. The second Cohen model does not have any either, although the proof is slightly more involved.
In either case, countable choice fails, and there are Dedekind-finite sets. In the latter case, countable choice from families of pairs fails as well.