Sorry, no online dictionaries contain the exact phrase double extension set theory.
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Reverse dictionary results:
1. supersymmetry
 2. cycle
3. selection
4. det
5. sets
6. wave mechanics
7. coextensive
8. construct
9. ism
10. group
 11. multiverse
12. union
13. breadth
14. return
15. over
16. rule
17. axis
18. resonance
19. sharp
20. section
 21. vantage
22. projection
23. returning
24. returns
25. fold
26. apposition
27. grow
28. inflation
29. trick
30. line
 31. amplification
32. hunch
33. prove
34. domain
35. form
36. advance
37. focus
38. shoot
39. tuism
40. advancing

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You can look up the words in the phrase individually using these links:   double ?   extension ?   set ?   theory ?
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