Enum BigFiveSystem 

pub enum BigFiveSystem {
    RCA0,
    WKL0,
    ACA0,
    ATR0,
    Pi11CA0,
}

The Big Five subsystems of second-order arithmetic, ordered by strength.

Variants

RCA0

Recursive Comprehension Axiom (weakest).

WKL0

Weak König’s Lemma.

ACA0

Arithmetical Comprehension Axiom.

ATR0

Arithmetical Transfinite Recursion.

Pi11CA0

Π¹_1 Comprehension Axiom (strongest).

Implementations

impl BigFiveSystem

pub fn name(&self) -> &'static str

Human-readable name of the system.

pub fn at_least_as_strong_as(&self, other: &BigFiveSystem) -> bool

Is this system stronger than or equal to the other?

pub fn proof_theoretic_ordinal(&self) -> &'static str

The corresponding proof-theoretic ordinal (Bachmann–Howard notation as string).

pub fn wkl0_is_conservative_over(&self) -> bool

Returns true if WKL₀ is Π¹_1-conservative over this system. This holds precisely for RCA₀.

Trait Implementations

impl Clone for BigFiveSystem

fn clone(&self) -> BigFiveSystem

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for BigFiveSystem

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl Hash for BigFiveSystem

fn hash<__H: Hasher>(&self, state: &mut __H)

Feeds this value into the given Hasher.

fn hash_slice<H>(data: &[Self], state: &mut H)

where H: Hasher, Self: Sized,

Feeds a slice of this type into the given Hasher.

impl Ord for BigFiveSystem

fn cmp(&self, other: &BigFiveSystem) -> Ordering

This method returns an Ordering between self and other.

fn max(self, other: Self) -> Self

where Self: Sized,

Compares and returns the maximum of two values.

fn min(self, other: Self) -> Self

where Self: Sized,

Compares and returns the minimum of two values.

fn clamp(self, min: Self, max: Self) -> Self

where Self: Sized,

Restrict a value to a certain interval.

impl PartialEq for BigFiveSystem

fn eq(&self, other: &BigFiveSystem) -> bool

Tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl PartialOrd for BigFiveSystem

fn partial_cmp(&self, other: &BigFiveSystem) -> Option<Ordering>

This method returns an ordering between self and other values if one exists.

fn lt(&self, other: &Rhs) -> bool

Tests less than (for self and other) and is used by the < operator.

fn le(&self, other: &Rhs) -> bool

Tests less than or equal to (for self and other) and is used by the <= operator.

fn gt(&self, other: &Rhs) -> bool

Tests greater than (for self and other) and is used by the > operator.

fn ge(&self, other: &Rhs) -> bool

Tests greater than or equal to (for self and other) and is used by the >= operator.

impl Eq for BigFiveSystem

impl StructuralPartialEq for BigFiveSystem