Pseudo algebraically closed field

In mathematics, a field is pseudo algebraically closed if it satisfies certain properties which hold for any algebraically closed field. The concept was introduced by James Ax in 1967.[1]

Formulation

A field K is pseudo algebraically closed (usually abbreviated by PAC[2]) if one of the following equivalent conditions holds:

Examples

Properties

References

  1. 1 2 Fried & Jarden (2008) p.218
  2. 1 2 Fried & Jarden (2008) p.192
  3. Fried & Jarden (2008) p.449
  4. Fried & Jarden (2008) p.196
  5. Fried & Jarden (2008) p.380
  6. Fried & Jarden (2008) p.209
  7. 1 2 Fried & Jarden (2008) p.210
  8. Fried & Jarden (2008) p.462
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