2026 survey on the value of the continuum
At the 2026 annual Tarski dinner, a survey was given to the attendees as to their view on the cardinality of the continuum. Here were the results:
| Votes | Response |
|---|---|
| 1 | $\aleph_2$ |
| 1 | $\aleph_{17}$ |
| 1 | $2^{\aleph_0}$ is not a set. |
| 1 | The question does not make sense. |
| 2 | There is not a definite answer to the question. |
| 3 | $2^{\aleph_0}$ is not well-orderable. |
| 6 | There is a definite answer to the question, but I do not have an opinion on the value. |
| 7 | Any natural and sufficiently powerful framework of theories deciding all sentences of the language of set theory, such as those arising from forcing axioms, determinacy, or V=Ultimate-L, should have good translations and interpretations into each other that preserve meaning. All our flowers bloom in the same garden. Can't we all just get along? |
Some historical context:
Various surveys of set theorists have been conducted over the years about their views concerning the cardinality of the continuum. One famous survey was conducted at the 1967 Summer Institute in Axiomatic Set Theory at UCLA. A more recent survey is currently being done by Sandra Müller, Ralf Schindler, and others for inclusion in the forthcoming book To Infinity and Beyond. The Continuum Problem in Modern Set Theory.
The Berkeley Continuum Meter is set to the current consensus among Berkeley set theorists about the cardinality of the continuum. The Berkeley Continuum Committee is tasked with keeping its value updated to track their evolving views. Some of the history of the continuum meter is described here: "After oscillating furiously in the 1960's and 1970's, the Berkeley Continuum Meter settled on $2^{\aleph_0} = \aleph_2$ for a large part of the 1980's and 1990's with occasional dips to $2^{\aleph_0} = \aleph_1$." More recently, the meter had stabilized for a longer period at $2^{\aleph_0} = \aleph_1$ following Hugh Woodin's work on Ultimate-$\mathsf{L}$.
