Math 2.0

Subjects

03 Mathematical logic and foundations

See MSC 03 on zbMATH Open.

NameTagKindMSC
Quotient set0011MTQMR6concept03E20
Countably infinite set00CR00C9DNconcept03E10
Power set00E0YZCERHconcept03E20
Every vector space has a basis00MS9VMQ9Zstatement15A03, 03E25
Preimage of a set01AHG4G9RTconcept03E20
Well-ordering principle01BX15HSRRstatement03F30
Composition of injections is injective01FPXMTBX1statement03E20
Order of cardinals01GTP8M5RGdefinition03E10
Equivalence classes form a partition01HT2CH8BHstatement03E20
Antisymmetric relation01MGYYBB9Rdefinition03E20
Infinite set01MKW4R283definition03E10
Surjective function01RVCMSN5Nconcept03E20
Composition of relations01SWBKDAWAdefinition03E20
Countable set01TQB88H4Cconcept03E10
Bijective iff it has a two-sided inverse01VG2A0BHWstatement03E20
Constructive proof01XM7JEKHYconcept03F65
Order of cardinals022RSX714Vconcept03E10
Well-founded relation0230ECX1Q5definition03E20
Left inverse02486SD328definition03E20
Conjunction025YZN3VJWconcept03B05
Negation029JBBF693concept03B05
Cardinality of a finite set02CK6QMXYDconcept03E10
Range of a function03FHD14RKCconcept03E20
Zorn's lemma04RXTQA5ZAstatement03E25
Contrapositive04T1CT7212statement03B05
Tautology05006AJ7DZconcept03B05
Cardinality of a finite set05099E1NMJdefinition03E10
The real numbers are uncountable0518MM6BE1statement03E10
Converse relation054K3HNN5Zconcept03E20
Binary relation05AVARPXA2concept03E20
Union of a family of sets05GK32H72Hdefinition03E20
Transitive closure05J9NWX07Xconcept03E20
Family of sets05Q6G4EH2Gdefinition03E20
Truth table05RSK4Q657concept03B05
Left inverse05SG20AMXHconcept03E20
Negation of an existential statement05SZQKH75Kstatement03B10
Set difference05WTQ6FFPSconcept03E20
Symmetric relation061J5VGSPTconcept03E20
The integers are countable066RJJVWH9statement03E10
Logical equivalence06GYGS41JKdefinition03B05
Multiplication of natural numbers06J5DE801Pconcept03F30
Disjunctive normal form06S4WGSEQAdefinition03B05
Finite set070R982G4Bconcept03E10
Correspondence between equivalence relations and partitions074482Q7CDstatement03E20
The reals have the cardinality of the continuum075PM9FH7Astatement03E10
Conjunctive normal form07C4A8Y18Kdefinition03B05
Composition of surjections is surjective07EH4R3RVQstatement03E20
Function composition07HF9YCWPPdefinition03E20
Union07KVB4JSC7definition03E20
Image of a set07XF282NWHconcept03E20
Equivalence class082RMRSY26definition03E20
Successor function0832XVR512definition03F30
Intersection of a family of sets0839XNQXDKdefinition03E20
Predicate logic086QKPF0A6concept03B10
Binary relation08EJC6Q25Hdefinition03E20
Equinumerous sets08EJHHMB5Rdefinition03E10
Product of countable sets is countable08G4XH86JCstatement03E10
Distributive laws for sets08N6EVA7DVstatement03E20
Partition of a set08QMKTWF9Tconcept03E20
Domain093CM69AGSdefinition03E20
Converse09A3N7ZN5Gconcept03B05
Necessary and sufficient conditions09BJQQB3VSconcept03B05
Partition of a set09CCE86A6Ddefinition03E20
Cartesian product09CEDJYBKPconcept03E20
Propositional logic09K9MWD2QQconcept03B05
Injective function09NWETVTNYconcept03E20
De Morgan's laws09PKJKA6J0statement03B05
Schröder–Bernstein theorem0A9V6RKQG6statement03E10
Successor function0AK9TGSNXYconcept03F30
Mathematical induction0ASJVEFA9Jconcept03F30
Equinumerous sets0B0KR7FH2Qconcept03E10
Complement0B1FSS1VZWdefinition03E20
Conjunctive normal form0B3D4C8YF2concept03B05
Universal quantifier0B88PQTJ66definition03B10
Finite set0BBTH3YSZAdefinition03E10
Power set0BC7KX51Z8definition03E20
Subset0BJR9QR08Econcept03E20
Universal set0BPYRMHJ48definition03E20
Set0BSJ7RQ9BWconcept03E20
Family of sets0C21Q694AGconcept03E20
Associativity of addition0C32J27WQCstatement03F30
Codomain0C5SR4FC74concept03E20
Cartesian product0C81YBVTWHdefinition03E20
Transitive relation0CYRECG2YQdefinition03E20
Tautology0D1AHYPM8Ndefinition03B05
Restriction of a function0D2MXBV21Tdefinition03E20
Zero is not a successor0D752BG155statement03F30
Right inverse0DDPZAG5ERdefinition03E20
Commutativity of addition0DFZNHJ0S2statement03F30
Well-founded relation0DQPNJNPYKconcept03E20
The rationals are countable0DS9KWFDK2statement03E10
Definition by recursion0DSHAVH45Fconcept03E20
Set difference0DT0TCV75Ndefinition03E20
Range of a function0E9GTAV478definition03E20
Cardinal number0EBACQFAZWconcept03E10
Empty set0ECVK59Y03object03E20
Function0EPAT51DXQconcept03E20
Element0EZ758XE73definition03E20
Disjunction0F72FK8EKBconcept03B05
Codomain0F9JHP8AJNdefinition03E20
Subset0FE8Q5S42Ydefinition03E20
Preimage of a set0FGCFY1AZXdefinition03E20
Identity function0FSNQ0GNCCdefinition03E20
Choice function0FWBQ53MPJconcept03E25
Order of quantifiers0FYQMKFE77concept03B10
Cardinality0G0ASKNA6Zconcept03E10
Equivalence relation0G8VEZ3WTKconcept03E20
Induction from an arbitrary base case0GF6AJEBZ0statement03F30
Bijective function0GG9TVW90Mconcept03E20
Universal quantifier0GHS47PDAQconcept03B10
Transitive relation0GJZW9JFZQconcept03E20
Cardinality of the power set0GPFKS96T7statement03E10
Disjunctive normal form0GVDFAY4KWconcept03B05
Disjunction0H5GKDTB01definition03B05
Intersection0HBRW4E6G1definition03E20
Zermelo–Fraenkel set theory0HE5WDQ9FJconcept03E30
Russell's paradox0HESMMSYEGstatement03E30
Order on the natural numbers0HNATXFEV5concept03F30
Axiom of choice0HTGB13FE2statement03E25
Injective iff it has a left inverse0HYFEEZAEMstatement03E20
Inverse function0J2WAR83WPconcept03E20
Associativity of composition0J6AKYZQT8statement03E20
Graph of a function0JBJYT69ZVconcept03E20
Converse relation0JCSQNNP2Mdefinition03E20
Logical equivalence0JMR2HM2N2concept03B05
Universal set0JNXSS9TJ9concept03E20
Ordered pair0JQWWFCS9Rdefinition03E20
Multiplication of natural numbers0JRC32D6K2definition03F30
Cardinality0JTGRV4WT4definition03E10
Existential quantifier0JW2FHW7G3definition03B10
Distributive law0KBEMAJAYAstatement03F30
Venn diagram0KCT6DPXJKconcept03E20
Hausdorff maximal principle0KM4KVR9MVstatement03E25
Strong induction0KMVFSHFGZstatement03F30
Equivalence relation induced by a function0KT8TGXD8Kconcept03E20
Antisymmetric relation0M0H1ZH8TTconcept03E20
Conjunction0M28ASWG8Tdefinition03B05
Symmetric difference0ME21QN125concept03E20
Continuum hypothesis0MN2MER9WNstatement03E50
Existential quantifier0MSRQHCNN9concept03B10
Well-ordering theorem0N109NG5ZXstatement03E25
Uniqueness quantifier0N3ADS4CHHdefinition03B10
Hilbert's hotel0N3Y8G340Xexample03E10
Symmetric relation0N9SA25Z3Vdefinition03E20
Restriction of a function0NF1KGDXX3concept03E20
Double negation law0NFAGWH84Kstatement03B05
Implication0NMG7W7Q11concept03B05
Cantor pairing function0NP5N5PYW5example03E10
Negation of a universal statement0P3A06QNDPstatement03B10
Transitive closure0PEJH7AC74definition03E20
Identity function0PSKT5W817concept03E20
Injective function0PVG1CRAJNdefinition03E20
Infinite set0PWE3BCHVJconcept03E10
Composition of relations0PYSR20HGFconcept03E20
Image of a set0Q3F20XB0Adefinition03E20
Domain0Q4CBD3HX0concept03E20
Uniqueness quantifier0QAJHFGZZJconcept03B10
Equivalence relation induced by a function0QE5PFJY7Vdefinition03E20
Peano axioms0QFT7Z76N5concept03F30
Predicate0QHEWQD30Bconcept03B10
Cardinal number0QKPNZKNEAdefinition03E10
Element0QM0T7T3PZconcept03E20
Indicator function0RCQZ36MMEconcept03E20
Ordinal number0RDJK7EQYYdefinition03E10
Complement0RKF1ZT5JJconcept03E20
Converse0RVYE75E2Mdefinition03B05
Every infinite set has a countably infinite subset0RWQ5VZ6VQstatement03E10
Image of an intersection0RX7DDBYCKstatement03E20
Law of excluded middle0RYYK8PG4Sstatement03B05
Addition of natural numbers0S13V32CPBconcept03F30
Biconditional0S6GMNJ62Yconcept03B05
Countably infinite set0SEZ3JGZP7definition03E10
Equivalence relation0SGTMBEWRFdefinition03E20
Set0SJ3RX9TXAdefinition03E20
Bijective function0SNQEF7Z53definition03E20
Predicate0T3DPBG981definition03B10
Axiom of extensionality0TB16T2C97statement03E30
The successor function is injective0TBYMWPWWBstatement03F30
Function composition0THBK9V825concept03E20
Set-builder notation0TMZ89Q5KAconcept03E20
Surjective iff it has a right inverse0TYQNHVB4Cstatement03E20
Aleph-null0V2H5PGJ9Bobject03E10
Vacuous truth0V4QXPGJQKconcept03B05
Biconditional0V6GAWTBYWdefinition03B05
De Morgan's laws for sets0VK0W4D5Y5statement03E20
Indicator function0VSB0XF4G7definition03E20
Disjoint sets0W4RPA8QH3definition03E20
Addition of natural numbers0W5DSDFQ4Gdefinition03F30
Inverse function0W766JAPSNdefinition03E20
Uncountable set0W7FBYS1F1concept03E10
Equivalence class0W95W33CMPconcept03E20
Cardinality of the continuum0WC28W9DNMobject03E10
Ordered pair0WFCNG0MZCconcept03E20
Cantor's theorem0WTEMGYV2Cstatement03E10
Right inverse0WWRD82HD2concept03E20
Union0X1GSWNBN1concept03E20
Uncountable set0X55M9XET4definition03E10
Reflexive relation0X8NMST0J2concept03E20
Cantor's diagonal argument0XCH8QVDCQconcept03E10
Reflexive relation0XEGNW851Sdefinition03E20
Function0XHDTE5YMZdefinition03E20
Surjective function0XKH881BZ7definition03E20
Negation0XR7A7RSXBdefinition03B05
Disjoint sets0XZ37KAB1Zconcept03E20
Graph of a function0Y0KFHF47Gdefinition03E20
Modus ponens0Y0MQYST0Mconcept03B05
Order on the natural numbers0Y9H52BT03definition03F30
Comparability of cardinals0YBHSJMN3Jstatement03E10
Ordinal number0YSCSX5YZCconcept03E10
Choice function0YXEQWRGP0definition03E25
Symmetric difference0Z49NTR1DZdefinition03E20
Countable union of countable sets is countable0Z8FM54P86statement03E10
Countable set0ZG61TFBESdefinition03E10
Proposition0ZGC7ZESYNconcept03B05
Transfinite induction0ZHQMQ2C1Nstatement03E10
Intersection0ZNMMA9TF5concept03E20
Implication0ZNX6DQ3EJdefinition03B05
Quotient set0ZVHXDSZC7definition03E20