452:
234:
243:
490:
475:
258:
248:
145:
470:
352:
123:
495:
347:
158:
202:
108:
52:
392:
268:
219:
197:
192:
278:
372:
207:
83:
180:
337:
163:
431:
376:
302:
253:
239:
8:
327:
308:
118:
457:
412:
382:
314:
297:
227:
130:
113:
88:
451:
402:
283:
263:
103:
417:
93:
44:
427:
406:
168:
137:
273:
98:
50:
484:
356:
40:
437:
366:
362:
28:
331:
67:
24:
441:
71:
75:
421:
396:
341:
290:
62:
386:
144:
With the
Zermelo–Fraenkel axioms above, this makes up the system
36:
19:
74:. They can be easily adapted to analogous theories, such as
60:
Together with the axiom of choice (see below), these are the
43:. Individual axioms are almost always part of a larger
148:
in which most mathematics is potentially formalisable.
225:
447:
213:
482:
483:
152:
174:
13:
476:Minimal axioms for Boolean algebra
136:
14:
507:
186:
66:standard axioms for contemporary
450:
235:Von Neumann–Bernays–Gödel axioms
321:
259:Axiom of projective determinacy
214:Alternates incompatible with AC
35:is understood differently; see
471:Axiomatic quantum field theory
23:as that term is understood in
1:
353:Fundamental axiom of analysis
124:Axiom schema of specification
249:Freiling's axiom of symmetry
159:Hausdorff maximality theorem
55:without the axiom of choice)
7:
464:
289:
203:Boolean prime ideal theorem
109:Axiom schema of replacement
10:
512:
491:Mathematics-related lists
393:Kuratowski closure axioms
269:Axiom of constructibility
220:Axiom of real determinacy
198:Axiom of dependent choice
193:Axiom of countable choice
348:Dirac–von Neumann axioms
317:(10 axioms and 1 schema)
208:Axiom of uniformization
84:Axiom of extensionality
53:Zermelo–Fraenkel axioms
181:Axiom of global choice
338:Axiom of countability
164:Well-ordering theorem
432:quantum field theory
377:quantum field theory
279:Kripke–Platek axioms
254:Axiom of determinacy
240:Continuum hypothesis
496:Mathematical axioms
373:Haag–Kastler axioms
328:Axiom of Archimedes
119:Axiom of regularity
458:Mathematics portal
413:Probability axioms
298:Parallel postulate
244:its generalization
228:mathematical logic
131:Zermelo set theory
114:Axiom of power set
89:Axiom of empty set
303:Birkhoff's axioms
284:Diamond principle
153:Equivalents of AC
104:Axiom of infinity
503:
460:
455:
454:
418:Separation axiom
309:Hilbert's axioms
226:Other axioms of
175:Stronger than AC
94:Axiom of pairing
45:axiomatic system
511:
510:
506:
505:
504:
502:
501:
500:
481:
480:
467:
456:
449:
428:Wightman axioms
407:natural numbers
383:Huzita's axioms
324:
315:Tarski's axioms
294:
231:
216:
189:
177:
155:
141:
138:Axiom of choice
57:
12:
11:
5:
509:
499:
498:
493:
479:
478:
473:
466:
463:
462:
461:
446:
445:
435:
425:
415:
410:
403:Peano's axioms
400:
390:
380:
370:
360:
350:
345:
335:
323:
320:
319:
318:
312:
306:
300:
293:
288:
287:
286:
281:
276:
274:Rank-into-rank
271:
266:
264:Martin's axiom
261:
256:
251:
246:
237:
230:
224:
223:
222:
215:
212:
211:
210:
205:
200:
195:
188:
187:Weaker than AC
185:
184:
183:
176:
173:
172:
171:
166:
161:
154:
151:
140:
135:
127:
126:
121:
116:
111:
106:
101:
99:Axiom of union
96:
91:
86:
56:
49:
9:
6:
4:
3:
2:
508:
497:
494:
492:
489:
488:
486:
477:
474:
472:
469:
468:
459:
453:
448:
443:
439:
436:
433:
429:
426:
423:
419:
416:
414:
411:
408:
404:
401:
398:
394:
391:
388:
384:
381:
378:
374:
371:
368:
364:
361:
358:
357:real analysis
354:
351:
349:
346:
343:
339:
336:
333:
329:
326:
325:
316:
313:
310:
307:
304:
301:
299:
296:
295:
292:
285:
282:
280:
277:
275:
272:
270:
267:
265:
262:
260:
257:
255:
252:
250:
247:
245:
241:
238:
236:
233:
232:
229:
221:
218:
217:
209:
206:
204:
201:
199:
196:
194:
191:
190:
182:
179:
178:
170:
167:
165:
162:
160:
157:
156:
150:
149:
147:
139:
134:
132:
125:
122:
120:
117:
115:
112:
110:
107:
105:
102:
100:
97:
95:
92:
90:
87:
85:
82:
81:
80:
79:
77:
73:
69:
64:
61:
54:
48:
46:
42:
41:self-evidence
38:
34:
30:
26:
22:
21:
438:Action axiom
367:sheaf theory
363:Gluing axiom
322:Other axioms
169:Zorn's lemma
143:
142:
128:
65:
59:
58:
32:
29:epistemology
17:
15:
332:real number
311:(20 axioms)
68:mathematics
31:, the word
25:mathematics
485:Categories
442:praxeology
305:(4 axioms)
72:set theory
16:This is a
129:See also
76:mereology
465:See also
422:topology
397:topology
342:topology
291:Geometry
63:de facto
51:ZF (the
18:list of
387:origami
20:axioms
37:axiom
33:axiom
27:. In
242:and
39:and
146:ZFC
70:or
487::
133:.
47:.
444:)
440:(
434:)
430:(
424:)
420:(
409:)
405:(
399:)
395:(
389:)
385:(
379:)
375:(
369:)
365:(
359:)
355:(
344:)
340:(
334:)
330:(
78:.
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.