Zermelo–Fraenkel set theory - 2026 ACF Regionals

Packet J: Tossup 11

In 2020, Scott Aaronson conjectured that the busy beaver function of 20 was the upper bound of what this system could prove. (-5[1])Shelah showed (10[1])that two implications of this system (10[1])produce contradictory answers to the Whitehead problem. (10[1])The first-order form (10[1])of this system violates the Löwenheim–Skolem (-5[1])theorem, (-5[2])leading to Skolem’s (10[1])paradox. (10[2])In 1963, Paul Cohen used forcing (10[1]-5[1])to show (10[1])that this system (10[5])and the continuum (10[1])hypothesis (10[4])are independent (10[1])of each other. (10[5])This (10[1])system’s (10[3])inclusion (10[1])of (10[1])the axiom of specification (10[2])allows (10[1])it to avoid (10[1]-5[1])Russell’s paradox. (10[2]-5[1])The letter (-5[1])C (-5[1])is appended (10[1])to this (10[1])system’s (10[1])name (10[2])to indicate (10[2])its inclusion (10[1])of the axiom (10[1])of (10[1])choice. (10[1])For 10 points, (10[1])name this standard formulation of set theory (10[2])proposed (10[1])by two German mathematicians, (10[1])often (10[1])known (10[1])by a two-letter (10[2])acronym. (10[1]) (10[5]0[24])■END■

ANSWER: Zermelo–Fraenkel set theory [or ZF; accept answers referring to Zermelo–Fraenkel set theory equipped with the axiom of choice or ZFC; prompt on set theory or axioms of set theory]

<Southampton A, Other Science> | Packet J - Southampton A, Indiana A, Illinois B, Edinburgh A

= Average correct buzzpoint

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Buzzes

Player	Team	Opponent	Buzzpoint	Value
Denis Liu	Stanford B	Stanford A	21	-5
Samuel Lipsutz	Chicago E	Chicago A	23	10
Oliver West	Cambridge C	LSE	29	10
Aiden Bang	Johns Hopkins B	John Jay	36	10
Ted Harrison	Edinburgh B	Bristol	39	10
Rohan Dalal	Georgia Tech A	Minnesota A	45	-5
Anuttam Ramji	Berkeley B	Berkeley A	46	-5
Abby Smith	Berkeley C	Berkeley D	46	-5
Eric Morshed	Johns Hopkins A	Columbia A	49	10
Stefan Stealey-Euchner	Arizona State	UCLA B	50	10
Akshay Seetharam	Claremont	Washington B	50	10
Kevin Ye	Simon Fraser	Toronto C	56	10
Stephen Walsh	Northwestern B	Indiana B	56	-5
Mattias Ehatamm	Maryland A	NYU A	58	10
Kaiwen Xiao	UCLA A	UC Irvine	61	10
Emmanuel Alayande	Florida B	Central Florida C	61	10
Philip Yao	Brown	Dartmouth B	61	10
Surya Dinesh	MIT	Yale	61	10
Matthew Sumanen	Georgia Tech C	Georgia Tech B	61	10
Eveline Ong	Oxford A	Imperial C	64	10
Asha Basu	McGill A	Waterloo B	65	10
Matthew Wang	UBC A	Waterloo A	65	10
Brian Hoff	Cornell B	Cornell A	65	10
Cade Reinberger	RIT	Penn State	65	10
Athena Shadden	Texas A	Texas B	67	10
Colin Veevers	Ottawa	Toronto B	70	10
Dennis Yang	Michigan B	Michigan State	70	10
Jake Meltzer	CWRU A	Michigan C	70	10
Noah Chin	Virginia Tech A	North Carolina C	70	10
Matthew Westley	Purdue A	Notre Dame B	70	10
Max Neal	Harvard B	Brandeis B	71	10
Coby Tran	Chicago C	Purdue B	72	10
Joy An	Harvard A	Southern Connecticut State	72	10
Zachary Joseph	Columbia B	NYU B	72	10
Adam Iqbal	Durham	Oxford B	73	10
Ben Hellman	Swarthmore	Georgetown	74	10
Kerry Xu	UCSD B	UCSD A	78	10
Amir Dolansky	Toronto E	Guelph	78	10
Tianyi Zheng	UCSD C	UC Santa Barbara	79	10
John McQueen	South Carolina A	Virginia Tech B	82	-5
Oscar O'Flanagan	Imperial A	UCL	82	10
Calvin Bostleman	Ohio State A	Ohio State C	84	10
Ariel Faeder	Pittsburgh	CWRU B	84	-5
John Mitnik	Columbia C	Rutgers B	84	10
Parker McCoig	Tennessee A	Georgia Tech D	86	-5
Raymond Jiang	Illinois C	Indiana C	87	-5
Abbott Sherwin	NC State A	Liberty B	89	10
Zaid Asif	NYU C	Vassar	91	10
June Miller	Florida A	Central Florida A	92	10
Nicolaus Derikx	Carleton University	UBC B	93	10
Samarth Ram	Chicago B	Illinois A	93	10
Michał Gerasimiuk	Stanford A	Stanford B	95	10
Chris Yoo	William and Mary	VCU	95	10
Owen Banks	Duke	North Carolina A	97	10
Yashwanth Bajji	Michigan A	Ohio State B	100	10
Dustin Sanders	Chicago D	Northwestern D	101	10
Seth Allen	McMaster A	Queen's	102	10
Ian Parsons	Maryland C	Rutgers A	105	10
Swapnil Garg	Berkeley A	Berkeley B	112	10
Athan Juritsch	Toronto G	Western C	112	10
Joseph Chambers	Virginia	James Madison A	113	10
Jack Lewis	Bruin	WashU A	117	10
Samuel Zheng	Toronto D	Toronto Metropolitan	118	10
Jacob Finley	Notre Dame A	Northwestern C	119	10
Peyton Legg	Central Florida B	Florida C	122	10
Sawyer Smith	Mississipi State	Alabama B	122	10
Kevin Liu	Maryland B	Catholic	123	10
Rishabh Dave	Berkeley D	Berkeley C	124	0
Luke Sloan	McGill B	Brock	124	0
Milan Fernandez	Brock	McGill B	124	0
Sicheng Jiang	Toronto F	McMaster B	124	10
Yash Modi	Western B	Western A	124	0
Anthony Yin	CWRU B	Pittsburgh	124	0
Fionn O'Connor	South Carolina B	James Madison B	124	0
Summer Solis	James Madison B	South Carolina B	124	0
James Watson	Wake Forest	NC State B	124	0
Dan Rajaratnam	NC State B	Wake Forest	124	0
Nermeen Rahman	Indiana B	Northwestern B	124	0
Ayaan Jajodia	Dartmouth A	Brandeis A	124	10
Isaac Studley	Carleton College	Missouri B	124	0
Lucas Barnes	Missouri B	Carleton College	124	0
Puna Ekka	Minnesota A	Georgia Tech A	124	10
Kanyon Beck	Murray State A	Texas A&M A	124	0
Dwight Solano	Texas A&M A	Murray State A	124	0
Nathan Woolery	Louisville B	Alabama A	124	0
Tomas Ospina	Alabama A	Louisville B	124	0
S. A. Shenoy	Georgia Tech D	Tennessee A	124	10
Ben Tibbles	Sewanee	Tennessee B	124	0
Alina Moore	Tennessee B	Sewanee	124	0
Roy Yang	WashU B	Kentucky	124	0
Nihal Jacob	Kentucky	WashU B	124	0
Ben LaFond	Cambridge B	City St. George's	124	10
Eli O'Sick Johnson	Binghamton B	Binghamton A	124	0
Andrew Miller	Binghamton A	Binghamton B	124	0
Alan Li	Cornell C	Rochester	124	0
Kieran Freed	Rochester	Cornell C	124	0

Summary

Tournament	Edition	Match	Heard	Conv. %	Neg %	Avg. Buzz
California (North)	Main Site	✓	3	67%	100%	103.50
California (South)	Main Site	✓	4	100%	0%	67.00
Canada	Main Site	✓	12	83%	0%	88.30
Florida	Main Site	✓	3	100%	0%	91.67
Great Lakes	Main Site	✓	5	80%	20%	81.00
Lower Mid-Atlantic	Main Site	✓	9	56%	11%	92.80
Midwest	Main Site	✓	8	75%	25%	79.67
Northeast	Main Site	✓	5	100%	0%	77.80
Overflow	Main Site	✓	3	67%	33%	87.00
South Central	Main Site	✓	2	50%	0%	67.00
Southeast	Main Site	✓	8	50%	13%	106.00
UK	Main Site	✓	6	100%	0%	68.50
Upper Mid-Atlantic	Main Site	✓	9	100%	0%	76.89
Upstate NY	Main Site	✓	4	50%	0%	65.00