Description: In this note we list independence results which are not readily available from table 1.
Content: In this note we list independence results which are not readily available from table 1. In each case we give the form numbers, the relationship, the reference and the model or models.
| Forms | Set Theory | References | Models | |
|---|---|---|---|---|
| \(14 + 43 \not\to 1\) | \((ZF)\) | Mathias [1979], p 160 (due to Pincus) | \(\cal M40(\kappa)\), \(\cal N40\) | |
| \(52 + 65 \not\to 1\) | \((ZF^{0})\) | Pincus [1972b] | \(\cal N2\) | |
| \( 14 + 295 \not\to 296\) | \((ZF)\) | Pincus [1997] | \(\cal N48\)T | |
| \(14 + 295 \not\to 15\) | \((ZF)\) | Pincus [1997] | \(\cal N48\)T | |
| \(14 + 15 \not\to 1\) | \((ZF)\) | Pincus [1997] | \(\cal M1\) | |
| \(130 + 18 \not\to 128\) | \((ZF)\) | Brunner [1984f] | \(\cal N2\)T | |
| \(130 + 18 + 128 \not\to 9\) | \((ZF)\) | Brunner [1984f] | \(\cal N3\)T | |
| \(18 + 128 \not\to 13\) | \((ZF)\) | Brunner [1984f] | \(\cal M1\) | |
| \(163 +67 \not\to 10\) | \((ZF^{0})\) | Brunner [1982a] | \(\cal N2\) | |
| \(163 + 67 \not\to 164\) | \((ZF^{0})\) | Brunner [1982a] | \(\cal N2\) | |
| \(164 + 60 + 91 \not\to 133\) | \((ZF^{0})\) | Brunner [1982a] | \(\cal N3\) | |
| \(133 + 17 + 89 \not\to 62\) | \((ZF^{0})\) | Brunner [1982a] | \(\cal N1\) | |
| \(62 + 57 \not\to 9\) | \((ZF)\) | Sageev [1981]. See note 44 for a related result. | \(\cal M32\) | |
| \(52 + 43 \not\to 206\) | \((ZF)\) | Pincus/Solovay [1977] | \(\cal M27\) | |
| \(111 \not\to 373(3)\) | \((ZF^{0})\) | \(\cal N2^*(3)\) |
Howard-Rubin number: 1
Type: Summary
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